Integral of unknown difficulty

In summary, the conversation discusses a difficult integral problem involving a U substitution and a substitution involving a German mathematician's name rule. The problem was given by an instructor who did not check its difficulty and was later given back to the students to solve at home.
  • #1
Brandon O
2
0
Integral of unknown difficulty!

Homework Statement


integral of: 1/[4+5sin(2x)] dx

The Attempt at a Solution


U substitution on 2x gives u=2x
then du becomes 2dx so... du=2 dx
after that, i get

1/2 * int of: 1/[4+5sin(u)] du

from here, using v=5sin(u)
then: dv=5cos(u) du

this is where i get stuck. Did i start it off right or did I mess it up here? I don't need the answer to it, just a push in the right direction from the start ><
 
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  • #2


This type of integral is typically solved using the substitution [itex]y=\tan(u/2)[/itex].
 
Last edited:
  • #3


My friends and I bashed our heads together long enough to come up with that german guy's name rule.

This is something we haven't done or learned (even though its in chapter 8, which we have done).

Thanks PF ^_^

Our instructor pulled this problem from a... kind of a teacher problem dump website or maybe a book. He didn't check the difficulty on it and put it on the exam anyways. After the initial turn in, he gave them back to the students to do at home... there was a 6 day gap where we could do the problem (as well as the rest of the test).
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is a fundamental tool in calculus and is used to calculate the total value of a function over a given interval.

2. What is the purpose of finding the integral of unknown difficulty?

The purpose of finding the integral of unknown difficulty is to solve for the unknown function or determine its properties. It can also help in understanding the behavior of the function and making predictions about its values at different points.

3. How do you solve for the integral of unknown difficulty?

The process of solving for the integral of unknown difficulty involves using various techniques such as substitution, integration by parts, and partial fractions. It requires a deep understanding of calculus and practice to master these techniques.

4. What are the applications of finding the integral of unknown difficulty?

Finding the integral of unknown difficulty has various applications in physics, engineering, economics, and other fields. It is used to calculate areas, volumes, work, and other important quantities in real-world problems.

5. Is there a specific method for finding the integral of unknown difficulty?

No, there is no specific method for finding the integral of unknown difficulty. It depends on the complexity of the function and the available techniques. It is important to have a good understanding of calculus and choose the appropriate method for each problem.

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